## Microparticle movements in optical funnels and pods |

Optics Express, Vol. 19, Issue 6, pp. 5232-5243 (2011)

http://dx.doi.org/10.1364/OE.19.005232

Acrobat PDF (4608 KB)

### Abstract

Three-dimensional microparticle movements induced by laser beams with a funnel- and tubular pod-like structure, in the neighbourhood of the focal plane of an optical trapping setup, are experimentally studied. The funnel and pod beams constructed as coherent superpositions of helical Laguerre-Gaussian modes are synthesized by a computer generated hologram using a phase-only spatial light modulator. Particle tracking is achieved by in-line holography method which allows an accurate position measurement. It is experimentally demonstrated that the trapped particle follows different trajectories depending on the orbital angular momentum density of the beam. In particular applying the proposed pod beam the particle rotates in opposite directions during its movement in the optical trap. Possible applications of these single-beam traps for volumetric optical particle manipulation are discussed.

© 2011 Optical Society of America

## 1. Introduction

1. A. Ashkin, *Optical Trapping and Manipulation of Neutral Particles Using Lasers: A Reprint Volume With Commentaries* (World Scientific Publishing Company, 2006). [CrossRef] [PubMed]

2. M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys. **41**, 275–285 (2000). [CrossRef]

4. A. Jesacher, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Holographic optical tweezers for object manipulations at an air-liquid surface,” Opt. Express **14**, 6342–6352 (2006). [CrossRef] [PubMed]

5. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science **292**, 912–914 (2001). [CrossRef] [PubMed]

7. T. Alieva, E. Abramochkin, A. Asenjo-Garcia, and E. Razueva, “Rotating beams in isotropic optical system,” Opt. Express **18**, 3568–3573 (2010). [CrossRef] [PubMed]

8. E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. **16**, 842–848 (2006). [CrossRef]

9. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical cogwheel tweezers,” Opt. Express **12**, 4129–4135 (2004). [CrossRef] [PubMed]

10. K. Dholakia, M. P. MacDonald, P. Zemanek, and T. Cizmár, *Laser manipulation of cells and tissues methods in cell biology* (Elsevier, 2007), chap. Cellular and colloidal separation using optical forces, pp. 467–495. [CrossRef]

11. D. G. Grier and Y. Roichman, “Holographic optical trapping,” Appl. Opt. **45**, 880–887 (2006). [CrossRef] [PubMed]

12. M. J. Padgett, J. E. Molloy, and D. Mcgloin, eds., *Optical Tweezers: Methods and Applications* (CRC Press, 2010). [CrossRef]

12. M. J. Padgett, J. E. Molloy, and D. Mcgloin, eds., *Optical Tweezers: Methods and Applications* (CRC Press, 2010). [CrossRef]

5. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science **292**, 912–914 (2001). [CrossRef] [PubMed]

## 2. Beam design for the optical trap

**r**= (

*x, y*) being a transversal position vector,

*r*

^{2}=

*x*

^{2}+

*y*

^{2},

*w*(

*z*) =

*w*

_{0}(1 + (

*z/z*)

_{R}^{2})

^{1/2}, where

*w*

_{0}is the minimum beam waist at the propagation distance

*z*= 0,

*ζ*(

*z*) = arctan(

*z/z*) corresponding to Gouy phase, and

_{R}*R*(

*z*) =

*z*(1 + (

*z*/

_{R}*z*))

^{2}representing the wavefront curvature radius. Here

*p*and azimuthal index

*l*. This choice is explained by mode orthonormality, stability under the propagation through the isotropic paraxial systems (which besides a well-known limitations remain a good model for the conventional optical tweezers) and simple expression for the longitudinal component of the orbital angular momentum (OAM),

*J*, carried by one mode or their linear superposition [14

_{z}14. R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express **15**, 15214–15227 (2007). [CrossRef] [PubMed]

2. M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys. **41**, 275–285 (2000). [CrossRef]

4. A. Jesacher, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Holographic optical tweezers for object manipulations at an air-liquid surface,” Opt. Express **14**, 6342–6352 (2006). [CrossRef] [PubMed]

*J*= 18. The choice of the beam indices as well as its waist parameter is explained by the limitations of our experimental setup (named, laser power, numerical aperture of the objective, particle size, etc.) and is not relevant for further discussions.

_{z}*a*are constants, is given by the expression [15] It is easy to see that the OAM density for a single LG mode is proportional to the intensity distribution

_{p,l}*J*, is obtained by integration over the

_{z}*x*and

*y*coordinates:

*J*= ∑

_{z}_{p,l}±|

*a*

_{p,l}|

^{2}

*l*.

*J*= 18, and similar beam size as ℱ

_{z}_{1}. Moreover ℱ

_{2}belongs to the class of the spiral beams mentioned above. From the analysis of mode indices it can be concluded (see for example [6

6. E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. **47**, 1177 (2004). [CrossRef]

7. T. Alieva, E. Abramochkin, A. Asenjo-Garcia, and E. Razueva, “Rotating beams in isotropic optical system,” Opt. Express **18**, 3568–3573 (2010). [CrossRef] [PubMed]

_{2}performs clockwise rotation at

*π*/2 during free space propagation. The beam focusing accelerates the rotation near the focal plane. Notice that opposite rotation corresponds to the complex conjugate beam

_{1}and ℱ

_{2}. The nonuniform distribution of the OAM over the rings for ℱ

_{2}yields to the larger OAM density in some regions and smaller for others than for ℱ

_{1}. It is expected that particle plane rotation induced by ℱ

_{2}will be limited by the region with large OAM density and intensity distribution.

*z*= 0) as it can be appreciated from Fig. 2. For the numerical simulations we used the parameters corresponding to the experimental setup: a 100× microscope objective lens (MO) with 1.32 NA, wavelength

*λ*= 532 nm and 0.25× relay optics (telescope). Then a minimum beam waist value of

*w*

_{0}= 3

*μ*m is reached at the focal plane of the MO. As observed in Fig. 2, while the ℱ

_{1}and ℱ

_{3}beams remain invariant (except scaling), the ℱ

_{2}one presents an additional clockwise rotation yielding a double helix intensity structure. We also note, that since the diameter of the particle used in the experiments for the analysis of 3D movement is 10

*μ*m, then the average intensity distribution over the particle cross-section is almost the same for the beams ℱ

_{1}and ℱ

_{3}. Therefore the main difference in their interaction with the particle is the presence of the OAM in the case of ℱ

_{1}beam.

16. R. Ozeri, L. Khaykovich, N. Friedman, and N. Davidson, “Large-volume single-beam dark optical trap for atoms using binary phase elements,” J. Opt. Soc. Am. B **17**, 1113–1116 (2000). [CrossRef]

18. N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. **279**, 229–234 (2007). [CrossRef]

*d*away from the focal plane by modulating the input beam ℱ

*(r) with a spherical phase distribution where f is the focal length of the microscope objective lens and*

_{n}*n*is the refractive index of the medium (water in our case). Then several optical funnels focused at different distances can be combined to construct a tubular-like trap. In this work we consider the superposition of two optical funnels described as where

_{md}*a*

_{1,2}= |

*a*

_{1,2}|

*g*(

*d*

_{1,2}) is the weight complex function that takes into account the focusing shift. In particular, we study the 𝒫

_{1,1}and 𝒫

_{2,2}beams with

*d*= −20

*μ*m that yields a tubular pod-like structure near to the focal region as displayed in Fig. 3(a) and 3(b), respectively. The peculiarity of these beams lies in the change of the OAM sign of their part interacting with the particle. Thus, it is expected to observe the particle rotation at the opposite directions at different distances

*z*.

*z*= 0 (first row) and

*z*= −11

*μ*m (second row) are shown in Fig. 4.

## 3. Experimental implementation

*δ*= 19

*μ*m) operating in phase-only modulation, and Nd:YAG laser with wavelength

*λ*= 532 nm and 400 mW. Theory and experimental implementation of such systems are studied in [19

19. B. Sun, Y. Roichman, and D. G. Grier, “Theory of holographic optical trapping,” Opt. Express **16**, 15765–15776 (2008). [CrossRef] [PubMed]

20. E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A, Pure Appl. Opt. **9**, S267 (2007). [CrossRef]

*λ*= 532 nm and 10 mW) that replaces the conventional incandescent illuminator, see Fig. 5. Its irradiance is comparable to that of conventional microscope illumination and therefore it does not exert measurable forces on the illuminated particles (suspended in the sample). Light scattered by the sample is recorded by a CCD camera (pixel size of 4.6

*μ*m and 30 frames per second) in real time as an in-line hologram, which can be numerically analyzed in order to obtain the 3D particle position. In this work we use Rayleigh-Sommerfeld (RS) back-propagation for the in-line hologram reconstruction because it permits faster particle tracking. This technique was studied in detail for holographic video microscopy in [21

21. F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express **18**, 13563–13573 (2010). [CrossRef] [PubMed]

21. F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express **18**, 13563–13573 (2010). [CrossRef] [PubMed]

22. J. P. Kirk and A. L. Jones, “Phase-Only Complex-Valued Spatial Filter,” J. Opt. Soc. Am. **61**, 1023–1028 (1971). [CrossRef]

24. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A **24**, 3500–3507 (2007). [CrossRef]

24. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A **24**, 3500–3507 (2007). [CrossRef]

25. T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett. **34**, 34–36 (2009). [CrossRef]

22. J. P. Kirk and A. L. Jones, “Phase-Only Complex-Valued Spatial Filter,” J. Opt. Soc. Am. **61**, 1023–1028 (1971). [CrossRef]

*s*(

*x, y*) =

*a*(

*x, y*) exp[

*iϕ*(

*x, y*)], where

*a*(

*x, y*) and

*ϕ*(

*x, y*) are the amplitude and phase distribution respectively, can be encoded as a phase CGH with a transmittance function

*H*(

*x, y*) = exp[

*iψ*(

*a,*

*ϕ*)]. To obtain an appropriate dependence of

*ψ*(

*a,*

*ϕ*), function

*H*(

*x, y*) has to be represented as a Fourier expansion in the domain of

*ϕ*(

*x, y*). As demonstrated in [24

24. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A **24**, 3500–3507 (2007). [CrossRef]

*s*(

*x, y*) is recovered from first-order term of such Fourier expansion by using the following hologram phase modulation: provided that the condition

*J*

_{1}[

*f*(

*a*)] =

*a*is fulfilled for every value of amplitude

*a*(

*x, y*) in the interval [0, 1], by choosing the appropriate value of

*f*(

*a*) according to Bessel function

*J*

_{1}(

*ρ*). To isolate the encoded field

*s*(

*x, y*) from the other terms of the Fourier expansion it is necessary to perform spatial filtering by adding a linear carrier phase

*φ*= 2

_{c}*π*(

*u*

_{0}

*x*+

*v*

_{0}

*y*), with spatial frequencies (

*u*

_{0},

*v*

_{0}), to the phase of the encoded field. Fortunately, this spatial filtering can be optically achieved using the Keplerian telescope (4-f system), see Fig. 5, where the SLM is placed at the back focal plane of the first relay lens. Notice that the reconstruction of the encoded signal

*s*(

*x, y*) is performed by spatial filtering of the first-order difracction term in the CGH Fourier spectrum plane [24

**24**, 3500–3507 (2007). [CrossRef]

26. I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express **16**, 16711–16722 (2008). [CrossRef] [PubMed]

*φ*arising from the SLM non-flatness, mainly astigmatism and spherical aberration, was calibrated following the suggestions reported in [20

_{ab}20. E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A, Pure Appl. Opt. **9**, S267 (2007). [CrossRef]

27. Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. **45**, 3425–3429 (2006). [CrossRef] [PubMed]

28. C. López-Quesada, J. Andilla, and E. Martín-Badosa, “Correction of aberration in holographic optical tweezers using a Shack-Hartmann sensor,” Appl. Opt. **48**, 1084–1090 (2009). [CrossRef]

*ψ*(

*a*,

*ϕ*−

*φ*+

_{ab}*φ*) mod 2

_{c}*π*. Notice that aberrations such as coma and astigmatism mainly degrade the lateral trapping efficiency while the spherical aberration mostly degrades the axial trapping performance [27

27. Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. **45**, 3425–3429 (2006). [CrossRef] [PubMed]

28. C. López-Quesada, J. Andilla, and E. Martín-Badosa, “Correction of aberration in holographic optical tweezers using a Shack-Hartmann sensor,” Appl. Opt. **48**, 1084–1090 (2009). [CrossRef]

*λ*= 532 nm) to the CCD camera, see Fig. 5. Then it is possible to obtain a volumetric reconstruction of the trapping light by translating the coverslip with respect to the objective lens. This approach has been previously demonstrated in [29

29. Y. Roichman, I. Cholis, and D. G. Grier, “Volumetric imaging of holographic optical traps,” Opt. Express **14**, 10907–10912 (2006). [CrossRef] [PubMed]

_{1}(a), ℱ

_{2}(b) and ℱ

_{3}(c) and the optical pods 𝒫

_{1,1}(d) and 𝒫

_{2,2}(e), measured by translating the coverslip (see also Media 1). These experimental results are in good agreement with the numerical simulations displayed in Fig. 4. Nevertheless there exists a wavefront distortion due to the residual aberrations of the optical setup, which may be minimized by performing further wavefront correction as reported in [28

28. C. López-Quesada, J. Andilla, and E. Martín-Badosa, “Correction of aberration in holographic optical tweezers using a Shack-Hartmann sensor,” Appl. Opt. **48**, 1084–1090 (2009). [CrossRef]

## 4. Microparticle manipulation: experimental results

*μ*m diameter polystyrene sphere, Spherotech SPV-20-5 Lot W01) at the focal plane of the MO, which in this case is near to the upper covering glass in order to compensate the axial scattering force. Figure 7 shows the motion of the trapped particle along the multiringed beam profile following the exerted torques (see also Media 2 and Media 3). As expected, the particle is confined in the high-intensity circular fringes and rotates around the beam ℱ

_{1}axis whereas for the case of beam ℱ

_{2}it only rotates in the angular range limited by the nonzero OAM density. The trapping with the beam ℱ

_{3}does not produce any rotation due to zero OAM density.

*μ*m diameter polystyrene spheres (Duke Scientific Lot 9949) suspended in water, which is induced by the proposed trapping beams. The flow-cell thickness is about 120

*μ*m and the particle motion starts from the lower coverslip surface. Figure 8(a)–8(c) displays the particle’s tracking for the beams ℱ

_{1}, ℱ

_{2}and ℱ

_{3}, respectively. Although both beams ℱ

_{1}and ℱ

_{2}have the same OAM (

*J*= 18), they exert different forces and torques on the particle according to the geometry of their 3D intensity and OAM density distributions. This yields different types of helix-like trajectories, see Fig. 8(a) Media 4 and Fig. 8(b) Media 5. In contrast, the beam ℱ

_{z}_{3}does not transfer OAM and therefore the particle just goes up to the minimum beam waist plane (

*z*= 0), see Fig. 8(c). Notice that these trapping beams are displayed for the trap-region of interest, given between the lower coverslip surface at

*z*= −30

*μ*m and the focal plane

*z*= 0. Several video snapshots corresponding to the in-line holograms obtained for the case ℱ

_{1}, ℱ

_{2}and ℱ

_{3}are also showed in Fig. 8(d)–8(f). We underline that clockwise rotation direction is obtained for the complex conjugate beams

_{1}and ℱ

_{3}posses angular symmetry the particle may be trapped in any point of the plane where the light force is sufficient, while for the beam ℱ

_{2}there are two well-defined regions around the intensity maxima where it may happens. Moreover, due to the relatively big particle size, two particles can be simultaneously trapped by beam ℱ

_{2}following different helical channels as it is observed in Fig. 8(b) and 8(e). This may be useful for the organization of different sorting particle flows in the same cell for the observation of their interaction in the focal plane.

_{1,1}. Figure 9(a) together with Media 8 show the particle trajectory. For better visualization a cut-out view of the beam and the particle’s trajectory are represented in Fig. 9(b). The video snapshots, several of them are presented in Fig. 9(c), corresponding to the in-line holograms used for the 3D particle-tracking reconstruction are found in Media 9. In this case the particle describes a spiral trajectory from the starting point A [

*z*= −30

*μ*m, see Fig. 9(b)] with clockwise rotation (due to the

*z*= −25

*μ*m corresponding to the point B. At this point the particle is simultaneously trapped by both optical funnels

_{1}, which exert opposite torques over the particle according with their OAM value (

*J*= ∓18, respectively). Therefore the particle goes straight up until the point C, in which its interaction with the ℱ

_{z}_{1}becomes stronger. From the point C to D the particle, as expected, follows a new spiral trajectory with anticlockwise rotation. The relatively short elevation (with respect to the funnel trapping) of the particle during spiral movement (A–B and C–D tracks) is explained by the fact that only one half of the beam energy is participated in light-particle interaction in these regions. We underline that the movements of such particles, induced by the designed beams, have been systematically reproduced. For smaller polystyrene sphere the longer spiral trajectories are expected due to the lager longitudinal regions where the particle is trapped by only one of the funnels (

_{1}) composed the pod.

*z*. It could be useful for twisting of rod-like particles or filaments which ends are trapped in the regions with opposite OAM sign.

## 5. Conclusions

## Acknowledgments

## References

1. | A. Ashkin, |

2. | M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys. |

3. | K. Ladavac and D. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express |

4. | A. Jesacher, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Holographic optical tweezers for object manipulations at an air-liquid surface,” Opt. Express |

5. | L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science |

6. | E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. |

7. | T. Alieva, E. Abramochkin, A. Asenjo-Garcia, and E. Razueva, “Rotating beams in isotropic optical system,” Opt. Express |

8. | E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. |

9. | A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical cogwheel tweezers,” Opt. Express |

10. | K. Dholakia, M. P. MacDonald, P. Zemanek, and T. Cizmár, |

11. | D. G. Grier and Y. Roichman, “Holographic optical trapping,” Appl. Opt. |

12. | M. J. Padgett, J. E. Molloy, and D. Mcgloin, eds., |

13. | A. E. Siegman, |

14. | R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express |

15. | A. M. Caravaca-Aguirre and T. Alieva, “Orbital angular moment density of beam given as a superposition of Hermite-Laguerre-Gauss functions,” in “PIERS 2011, Marrakesh,” (2011). |

16. | R. Ozeri, L. Khaykovich, N. Friedman, and N. Davidson, “Large-volume single-beam dark optical trap for atoms using binary phase elements,” J. Opt. Soc. Am. B |

17. | J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. |

18. | N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. |

19. | B. Sun, Y. Roichman, and D. G. Grier, “Theory of holographic optical trapping,” Opt. Express |

20. | E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A, Pure Appl. Opt. |

21. | F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express |

22. | J. P. Kirk and A. L. Jones, “Phase-Only Complex-Valued Spatial Filter,” J. Opt. Soc. Am. |

23. | J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. |

24. | V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A |

25. | T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett. |

26. | I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express |

27. | Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. |

28. | C. López-Quesada, J. Andilla, and E. Martín-Badosa, “Correction of aberration in holographic optical tweezers using a Shack-Hartmann sensor,” Appl. Opt. |

29. | Y. Roichman, I. Cholis, and D. G. Grier, “Volumetric imaging of holographic optical traps,” Opt. Express |

**OCIS Codes**

(090.1760) Holography : Computer holography

(140.3300) Lasers and laser optics : Laser beam shaping

(140.7010) Lasers and laser optics : Laser trapping

(090.1995) Holography : Digital holography

**ToC Category:**

Optical Trapping and Manipulation

**History**

Original Manuscript: December 21, 2010

Revised Manuscript: February 10, 2011

Manuscript Accepted: February 13, 2011

Published: March 4, 2011

**Virtual Issues**

Vol. 6, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

José A. Rodrigo, Antonio M. Caravaca-Aguirre, Tatiana Alieva, Gabriel Cristóbal, and María L. Calvo, "Microparticle movements in optical funnels and pods," Opt. Express **19**, 5232-5243 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-6-5232

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### References

- A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers: A Reprint Volume With Commentaries (World Scientific Publishing Company, 2006). [CrossRef] [PubMed]
- M. Padgett, and L. Allen, "Light with a twist in its tail," Contemp. Phys. 41, 275-285 (2000). [CrossRef]
- K. Ladavac, and D. Grier, "Microoptomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004). [CrossRef] [PubMed]
- A. Jesacher, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, "Holographic optical tweezers for object manipulations at an air-liquid surface," Opt. Express 14, 6342-6352 (2006). [CrossRef] [PubMed]
- L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001). [CrossRef] [PubMed]
- E. G. Abramochkin, and V. G. Volostnikov, "Spiral light beams," Phys. Usp. 47, 1177 (2004). [CrossRef]
- T. Alieva, E. Abramochkin, A. Asenjo-Garcia, and E. Razueva, "Rotating beams in isotropic optical system," Opt. Express 18, 3568-3573 (2010). [CrossRef] [PubMed]
- E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, "Micro-object manipulations using laser beams with nonzero orbital angular momentum," Laser Phys. 16, 842-848 (2006). [CrossRef]
- A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, "Size selective trapping with optical cogwheel tweezers," Opt. Express 12, 4129-4135 (2004). [CrossRef] [PubMed]
- K. Dholakia, M. P. MacDonald, P. Zemanek, and T. Cizmár, Laser manipulation of cells and tissues methods in cell biology (Elsevier, 2007), chap. Cellular and colloidal separation using optical forces, pp. 467-495. [CrossRef]
- D. G. Grier, and Y. Roichman, "Holographic optical trapping," Appl. Opt. 45, 880-887 (2006). [CrossRef] [PubMed]
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